Showing papers by "John B. Moore published in 1991"

Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences.

Abstract: Techniques for characterizing very small single-channel currents buried in background noise are described and tested on simulated data to give confidence when applied to real data. Single channel currents are represented as a discrete-time, finite-state, homogeneous, Markov process, and the noise that obscures the signal is assumed to be white and Gaussian. The various signal model parameters, such as the Markov state levels and transition probabilities, are unknown. In addition to white Gaussian noise, the signal can be corrupted by deterministic interferences of known form but unknown parameters, such as the sinusoidal disturbance stemming from AC interference and a drift of the base line owing to a slow development of liquid-junction potentials. To characterize the signal buried in such stochastic and deterministic interferences, the problem is first formulated in the framework of a Hidden Markov Model and then the Expectation Maximization algorithm is applied to obtain the maximum likelihood estimates of the model parameters (state levels, transition probabilities), signals, and the parameters of the deterministic disturbances. Using fictitious channel currents embedded in the idealized noise, we first show that the signal processing technique is capable of characterizing the signal characteristics quite accurately even when the amplitude of currents is as small as 5-10 fA. The statistics of the signal estimated from the processing technique include the amplitude, mean open and closed duration, open-time and closed-time histograms, probability of dwell-time and the transition probability matrix. With a periodic interference composed, for example, of 50 Hz and 100 Hz components, or a linear drift of the baseline added to the segment containing channel currents and white noise, the parameters of the deterministic interference, such as the amplitude and phase of the sinusoidal wave, or the rate of linear drift, as well as all the relevant statistics of the signal, are accurately estimated with the algorithm we propose. Also, if the frequencies of the periodic interference are unknown, they can be accurately estimated. Finally, we provide a technique by which channel currents originating from the sum of two or more independent single channels are decomposed so that each process can be separately characterized. This process is also formulated as a Hidden Markov Model problem and solved by applying the Expectation Maximization algorithm. The scheme relies on the fact that the transition matrix of the summed Markov process can be construed as a tensor product of the transition matrices of individual processes.

Exponential convergence of a learning controller for robot manipulators

Abstract: The proof for the exponential convergence of a class of learning and repetitive control algorithms for robot manipulators is given. The learning process involves the identification of the robot inverse dynamics function by having the robot execute a set of tasks repeatedly. Using the concepts of functional persistence of excitation and functional uniform complete observability, it is shown that, when a training task is selected for the robot which is persistently exciting, the learning controllers are globally exponentially stable. Repetitive controllers are always exponentially stable. >

A Levinson-type algorithm for modeling fast-sampled data

Abstract: The standard discrete-time autoregressive model is poorly suited for modeling series obtained by sampling continuous-time processes at fairly rapid rates. Large computational errors can occur when the Levinson algorithm is used to estimate the parameters of this model, because the Toeplitz covariance matrix is ill-suited for inversion. An alternative model is developed based on an incremental difference operator, rather than the shift operator. It is shown that, as the sampling period goes to zero, unlike the standard autoregressive parameters, the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous-time process. A Levinson-type algorithm for efficiently estimating the parameters of this model is derived. Numerical examples are given to show that when the sampling interval is small this algorithm is considerably less sensitivity to arithmetic roundoff errors than the Levinson algorithm. >

Tracking randomly varying parameters: Analysis of a standard algorithm

Abstract: In linear stochastic system identification, when the unknown parameters are randomly time varying and can be represented by a Markov model, a natural estimation algorithm to use is the Kalman filter. In seeking an understanding of the properties of this algorithm, existing Kalman-filter theory yields useful results only for the case where the noises are gaussian with covariances precisely known. In other cases, the stochastic and unbounded nature of the regression vector (which is regarded as the output gain matrix in state-space terminology) precludes application of standard theory. Here we develop asymptotic properties of the algorithm. In particular, we establish the tracking error bounds for the unknown randomly varying parameters, and some results on sample path deviations of the estimates.

Adaptive lqg controller with loop transfer recovery

Abstract: SUMMARY In this paper we propose for scalar plants an adaptive LQG controller with adaptive input sensitivity function/loop transfer recovery of an associated adaptive LQ design. The sensitivity recovery can be viewed as a frequency-shaped loop recovery where the weights involve a sensitivity function. The adaptive loop/sensitivity recovery is achieved by feeding back the estimation residuals to the control through a stable bounded input, bounded output (BIBO) adaptive filter Q~. For simplicity we consider fixed but uncertain plants in the model set and identification schemes where there are consistent parameter estimates. For non-minimum phase plants an asymptotic partial recovery is achieved via a recursive least squares update of the BIBO filter Qk. The degree of recovery can be prescribed a priori between zero and the maximum possible. For the case of minimum phase plant estimates, full loop recovery may be achieved asymptotically by prescribing a maximum degree of recovery. The motivation for proposing the new adaptive control algorithm is to enhance robustness of adaptive LQG designs, taking advantage of the robustness enhancement properties of sensitivity/loop recovery for off-line designs. The robustness properties of the new algorithm are demonstrated by simulation results.

Adaptive disturbance rejection

Abstract: Using averaging analysis a novel direct adaptive algorithm applied to a linear plant is analyzed. The prior knowledge includes a nominal model and a stabilizing controller for the plant. It is shown that the stabilizing controller can be augmented with an adaptive controller solely aimed at disturbance rejection/trajectory following. The overall scheme retains the stability properties of the stabilizing (fixed) controller and improves its performance with respect to disturbance rejection and trajectory following. >

Kalman Filtering: Whence, What and Whither?

Abstract: Undoubtedly, one of the major contributions of R.E. Kalman has been the Kalman filter, [1,2], the magnitude of the contribution being specifically recognized in the award of the Kyoto Prize.

Signal processing of semi-Markov models with exponentially decaying states

Abstract: The authors straightforwardly modify hidden Markov model (HMM) processing, including the Baum-Welch reestimation formulae and related expectation maximization (EM) processing to deal with discrete-state, semi-Markov stochastic processes when their realizations are hidden (imbedded) in noise. They generalize such techniques to cope with exponential decay of states between step transitions. The motivation is that, in certain cases of biological signal processing, such models appear to be more appropriate than simpler ones. The time-varying transition probabilities of an underlying semi-Markov signal are unknown, 'exponential' decay rates between step transitions are unknown, and perhaps the noise statistics are not precisely known. >

Enhancing optimal controllers via techniques from robust and adaptive control

Abstract: A general framework to enhance the robustness of an optimal control law is presented, with emphasis on the nonlinear case. The framework allows a blending of offline nonlinear optimal control, online linear robust feedback control for regulation about the optimal trajectory, and online adaptive techniques to enhance performance/robustness. Some general fundamental stability properties are developed for the nonlinear plant and linear robust controller case. Performance enhancement results in the presence of unmodeled linear dynamics based on an averaging analysis. A convergence analysis based on averaging theory appears possible in principle for any specific nonlinear system. Certain model-reference adaptive control algorithms come out as special cases. A nonlinear optimal control problem is studied to illustrate the efficacy of the techniques, and the possibility of further performance enhancement based on functional learning is noted. >

Functional Learning in Optimal Non-linear Control

Abstract: This paper describes one approach to the application of functional learning techniques to assist in achieving near optimal control of nonlinear systems in the presence of disturbances and/or unmodelled dynamics. A standard approach to achieving robustness of open loop optimal control of nonlinear systems is to apply feedback control based on plant linearization and application of linear quadratic control methods. In earlier studies, it has been shown that such methods can be enhanced by augmenting with adaptive loops, achieving what is termed adaptive-Q control. Here, instead of the adaptive-Q filter being a linear system with coefficients adjusted by a least squares law, the filter's coefficients are functionally dependent on a subset of the optimal states associated with a nominal plant. The functional representation is updated by a least squares law in the case that `measurements' are linear in the function's unknown parameters, as when the function is represented by a sum of bisigmoids in the function input variable space. Such algorithms, and their convergence properties, have been previously studied in an identification context. A simulation study of the optimal quadratic regulation of the nonlinear 2-state Van der Pol equations is used to demonstrate improved performance in the presence of either a constant unknown disturbance of unmodelled dynamics, or stochastic disturbances. The approach could well have application in areas such as aircraft control or robot control where gain schedules are learnt on line. Such applications will be the subject of further study.

Hidden Markov model signal processing in presence of unknown deterministic interferences

Abstract: Expectation maximization (EM) algorithms are used to extract discrete-time finite-state Markov signals imbedded in a mixture of Gaussian white noise and deterministic signals of known functional form with unknown parameters. The authors obtain maximum likelihood estimates of the Markov state levels, state estimates, transition probabilities and also of the parameters of the deterministic signals. Specifically, they consider two important types of deterministic signals: periodic, or almost periodic signals with unknown frequency components, amplitudes and phases; and polynomial drift in the states of the Markov process with the coefficients of the polynomial unknown. The techniques developed here along with the supporting theory appear more elegant and powerful than ad hoc heuristic alternatives. >

Factorizations that relax the positive real condition in continuous-time ELS schemes

Abstract: This paper proposes Extended Least Squares (ELS) schemes for ARMAX model identification of continuous-time systems. The schemes have a relaxed Strictly Positive Real (SPR) condition for global convergence. The relaxed SPR scheme is achieved by introducing overparametrisation and prefiltering but without introducing ill-conditioning. The schemes presented are the first such proposed for continuous-time systems. The concepts developed here carry through to output-error, fast-sampled continuous-time systems and associated discrete-time ELS algorithms. We also state conditions for the persistence of excitation (P.E.) of the regression vectors in the proposed ELS schemes to assure strong consistency and obtain convergence rates.

Balancing matrix factorizations via gradient flow techniques and the singular value decomposition

Abstract: The authors explore various gradient flows on manifolds which converge exponentially to balanced matrix factorizations, of which the singular value decomposition is the most well known. Such flows are initialized on trivial nonbalanced factorizations. The authors look at flows for the transformation matrix given an initial factorization, as well as flows on matrix factor themselves. More general flows are given that allow the matrix being factorized to be parameter dependent. >